Degla, who thrashed Arab Contractors 4-1 in their opener, took the lead after nine minutes when Hani Hassan hit his own net.
But the hosts scored three goals in a row through Ahmed Abdul-Raouf, Hassan and Ayman Hefni.
After the break, Ghanaian striker Wisdom Agblexo pulled one back for Degla, but MCDR hit three on the trot once again. This time Ibrahim Toure, Ihab Mahrous and Mahmoud Touba scored.
Complacency
Degla coach Walter Meows believes that the famous victory over Contractors had a negative effect on his inexperienced team.
"Egyptian players become subject to an astonishing state of complacency after scoring a big win," the Belgian coach said.
"That’s exactly what happened to the players after the victory over Contractors last week."
Degla slipped to eighth place in the league table as MCDR moved to second.